Question

2. Dinesh and Mahesh are partners sharing profits and losses in the ratio of 3:2.
They admit Ramesh into business and the new ratio was agreed to be 5:4:3.
Calculate the sacrifice ratio.
(Ans: 11:4)​

Answer 1

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

Dinesh and Mahesh are partners sharing profits and losses in the ratio of 3 : 2 . They admit Ramesh into business and the new ratio was agreed to be 5 : 4 : 3 . Calculate the sacrifice ratio .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

• Sacrifice ratio of Dinesh and Mahesh = 11 : 4

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• Dinesh and Mahesh are partners sharing profits and losses in the ratio of 3 : 2 .

• They admit Ramesh into business and the new ratio was agreed to be 5 : 4 : 3 .

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• Sacrifice ratio of Dinesh and Mahesh

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

$\red{ \underline{ \underline{\textsf{Ratio before admitting Ramesh : }}}}$

Dinesh : Mahesh = 3 : 2

• Dinesh's Share = 3/5

• Mahesh's Share = 2/5

$\red{ \underline{ \underline{\textsf{Ratio after admitting Ramesh : }}}}$

Dinesh : Mahesh : Ramesh = 5 : 4 : 3

• Dinesh's Share = 5/12

• Mahesh's Share = 4/12

• Ramesh's Share = 3/12

$\red{ \underline{ \underline{\textsf{Sacrifice ratio : }}}}$

$\purple{ \boxed{ \textsf{Sacrifice ratio = Old ratio - New ratio}}}$

$\red{ \underline{ \underline{\textsf{Dinesh's Sacrifice : }}}}$

$\\ \displaystyle \footnotesize \longrightarrow \textsf{Ratio of Dinesh before admitting Ramesh - Ratio of Dinesh after admitting Ramesh} \\\ \\ \displaystyle \sf \longrightarrow \frac{3}{5} - \frac{5}{12} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{36 - 25}{60} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{11}{60} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\red{ \underline{ \underline{\textsf{Mahesh's Sacrifice : }}}}$

$\\ \displaystyle \footnotesize \longrightarrow \textsf{Ratio of Mahesh before admitting Ramesh - Ratio of Mahesh after admitting Ramesh} \\\ \\ \displaystyle \sf \longrightarrow \frac{2}{5} - \frac{4}{12} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{24 - 20}{60} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{4}{60} \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\red{ \underline{ \underline{\textsf{Sacrifice ratio of Dinesh and Mahesh : }}}}$

Dinesh's Sacrifice : Mahesh's Sacrifice

= 11/60 : 4/60

= 11 : 4

$\purple{\boxed{ \begin{array}{l} \textsf{Sacrifice ratio of Dinesh and Mahesh = 11 : 4 }\end{array}}}$